I've followed F1 for over thirty years and, to be quite honest, didn't really notice the branding behind it until it really became a brand in itself.
Despite that, I think the last two logos - pictured above - are both nice in their own way.
The old FIA version had a nice use of negative space with the racing car and wheels, and the current one (on the left, used to launch F1 very much as basically the jewel in the crown of car racing) also used negative space very well to create the 1.
Now that Bernie Ecclestone is gone and Liberty Media is in charge, there's talk of a new logo, with the three shown below the finalists.
And, well, yeah...they're not that inspiring.
I can see that the first two are trying to evoke a racing track, but they're a bit too literal - not to mention wonky. The first one looks like something from the 1970s, which I'd like if it was done well, but the F is too long and fat, while the 1 could also be an I (albeit a thin one). The typeface is...different. All in all, it already looks terribly dated.
The second one is perhaps - if I really must choose - my favourite. The typeface is non-threatening and the icon itself isn't that bad. If they really, really must change what has become something of an iconic logo, then this one would probably not be as hated as the others.
The last one is as uninspiring as they come. This is Formula One motor racing! The space at the top of the F and 1 look misaligned; my eyes are trying to find something in the negative space between the characters, but there's nothing there; and that's it! The characters have notches in them, for whatever reason, and the typeface is a Helvetica-looking kind of thing that I really can't be bothered to look up. I mean, it obviously represents F1 because it says so, but nothing about it suggests anything that you might associate with the sport.
Seriously, if this is the best they can come up with, I'm glad I no longer subscribe to a TV channel that has to pay the company to show the races.